Percent Growth Rate Calculator

What this calculator does

So, you have a value at the start and a value at the end of some number of years, and you want the average growth per year as a percentage. This tool gives you that. Enter the starting value, the ending value, and the number of years, and it returns the average annual percent growth rate.

Three inputs, one figure out: the yearly rate of growth on average across the period.

How to use it

1. Enter the past or present value, where things started.
2. Enter the present or future value, where they ended.
3. Enter the number of years, and press Calculate.

The two values need to be different, and the number of years must be more than zero.

The percent change first

The tool works in two steps, and the first is the total percent change over the whole period. It takes the ending value minus the starting value, divides by the starting value, and multiplies by 100. This gives the overall change as a percentage: how much bigger or smaller the value became in total. If something went from 100 to 150, the total change is 50 percent. A rise gives a positive percentage, and a fall gives a negative one.

Spreading it across the years

The second step turns that total into a yearly figure by dividing the total percent change by the number of years. If the value grew by 50 percent over 5 years, dividing gives 10 percent per year. This is the average annual growth rate: the single yearly percentage that describes how fast the value moved, on average, over the whole span. It is a handy summary figure when you want to compare growth across periods of different lengths.

A simple average, not compounded

It is worth being clear about how this tool defines the yearly rate, because there are two common ways. This tool uses the straightforward one: it divides the total change evenly across the years, a simple average. It does not compound, meaning it does not account for growth building on previous growth year after year. That approach, where each year's growth is calculated on the running total, gives a slightly different figure known as the compound annual growth rate. For a quick, evenly-shared sense of yearly change, the simple average this tool provides is clear and easy to interpret, and it is exactly what the calculation returns.

A worked example

Enter a starting value of 100, an ending value of 150, and 5 years. The total change is 150 minus 100, which is 50, divided by 100 and times 100, giving 50 percent overall. Dividing that by 5 years gives 10 percent per year. So the average annual growth rate is 10 percent.

Questions people ask

What does this tool calculate?

The average annual percent growth: the total percent change from start to end, divided by the number of years.

How is it worked out?

First the total percent change, from the difference over the starting value times 100, then that divided by the number of years.

Is this the compound annual growth rate?

No. This is a simple average that shares the total change evenly across the years, without compounding. The compound rate accounts for growth building on itself and differs slightly.

Can the rate be negative?

Yes. If the ending value is lower than the starting value, the change is negative, giving a negative average annual rate.

What about a percent of a percent?

That is a different calculation. The percent of a percent calculator multiplies two percentages together.

References

On percent change and growth. A percent growth rate is built from the percent change over a period, here averaged across the years.

1. Eric W. Weisstein, "Percent," from MathWorld, a Wolfram resource, on percentage change, including growth from a starting value to an ending value.
2. "Percentage," Wikipedia, on percentage change and its calculation.